A pole of height 75 m stands on top of a building. At a point on the ground, the angle of elevation of bottom of pole is 45° and the top of pole is 60°. What is the height of the building?
Answer & explanation
Correct answer: option 3
tan 45° = 1 : 1
(BC) (CD) = x
tan 60° = \(\sqrt {3}\) : 1
(AC) (CD)
↓ ↓
\(\sqrt {3}\)x = x
AB = AC - BC
75 = \(\sqrt {3}\)x - x
⇒ x = \(\frac{75}{\sqrt {3} - 1}\)
⇒ x =\(\frac{75}{2}\)(\(\sqrt {3}\) + 1) m